here is an OG problem in which i have a real doubt in

Question

here is an OG problem in which i have a real doubt in solving.

if n is a +ive integer, is (1/10)^n 2
b)(1/10)^(n-1) 2, (1/10)^3 is well clearly less than 0.01...hence dis statement is sufficient
 while considering the 2nd statement, i took n=1( bcoz 1 is the smallest +ive integer)
now that wud make n-1=0 an we know that (anything)^0=1 so if n=1 then this statement comes out false but if we take n=3, then this comes out true. so this statement is not sufficent. hence i selected option no 1 but this is incorrect..
plz help

subhashghosh · Answer

Hiya, if you decompose (2), you can see that : (1/10)^(n-1) <0.1 (1/10)^n * (1/10)^-1 <0.1 => (1/10)^n * 10 <0.1 => (1/10)^n < 0.01 This is what the question is asking, so no need to pick numbers.

Onell · Answer

+1 awesome post subashgosh

subhashghosh · Answer

Thanks a lot

fluke · Answer

(\frac{1}{10})^n < 0.01 \frac{1}{10^n} < 10^{-2} \frac{1}{10^n} < \frac{1}{10^2} Cross Multiply; 10^2<10^n Flip LHS and RHS and flip the inequality symbol from "<" to ">" 10^n>10^2 Bases are same, thus the question becomes; Is n>2? 1. n>2 . Sufficient. 2. (1/10)^(n-1) <0.1 (\frac{1}{10})^{(n-1)}<0.1 \frac{1}{10^{(n-1)}}<10^{-1} \frac{1}{10^{(n-1)}}<\frac{1}{10} Cross Multiply; 10<10^{(n-1)} Flip RHS and LHS and flip the inequality symbol from "<" to ">" 10^{(n-1)}>10 n-1>1 n>2. Sufficient. Ans: "D"

Marcab · Answer

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here is an OG problem in which i have a real doubt in

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